To solve the system of equations, we have:
- \( y = 2x - 3 \) (Equation 1)
- \( 4x - 3y = 31 \) (Equation 2)
We can use Equation 1 to substitute for \( y \) in Equation 2.
Substituting \( y \) in Equation 2:
\[ 4x - 3(2x - 3) = 31 \]
Now, simplify the equation:
\[ 4x - 6x + 9 = 31 \]
Combine like terms:
\[ -2x + 9 = 31 \]
Now, isolate \( x \):
\[ -2x = 31 - 9 \] \[ -2x = 22 \] \[ x = -11 \]
Now, substitute \( x = -11 \) back into Equation 1 to find \( y \):
\[ y = 2(-11) - 3 \] \[ y = -22 - 3 \] \[ y = -25 \]
So the solution to the system of equations is:
\((-11, -25)\)
Thus, the solution to the system is \((-11, -25)\).